Question: Simplify the following expression: $q = \dfrac{-3p^2 + 9p + 162}{p - 9} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ q =\dfrac{-3(p^2 - 3p - 54)}{p - 9} $ Then we factor the remaining polynomial: $p^2 {-3}p {-54} $ ${-9} + {6} = {-3}$ ${-9} \times {6} = {-54}$ $ (p {-9}) (p + {6}) $ This gives us a factored expression: $\dfrac{-3(p {-9}) (p + {6})}{p - 9}$ We can divide the numerator and denominator by $(p + 9)$ on condition that $p \neq 9$ Therefore $q = -3(p + 6); p \neq 9$